In this work, we consider minimal models of Riemannian foliations on connected, simply-connected manifolds following Lehmann. We show that if the minimal model has an underlying rational form of finite type, then it can be realized in rational homotopy by a fibration of finite CW complexes. As a consequence, based on results of Gottlieb and Chern-Hirzebruch-Serre, a signature product formula is obtained.In the second part, inspired by Hurder, basic dual homotopy invariants of Riemannian foliations are defined using minimal models. Existence and vanishing theorems are proved for these invariants.